If cos x-y-cos x-y-cos 7-t-cos 7-t-0 then tan x tan y tan 7 tan t-A- 1B- -1C- 2D- -2

The correct option is B 1 cos (x y)/cos(x+y)+cos (7+t)/cos (7 t)=0 ⇒1+tan x tan y/1 tan x tan y+1 tan 7 tan t/1+tan 7 tan t=0 ⇒ (1+tan 7 tan t +ta ...

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Byju's Answer

Standard XI

Mathematics

Conditional Identities

If cos x-y/co...

Question

If $\frac{c o s (x - y)}{c o s (x + y)} + \frac{c o s (7 + t)}{c o s (7 - t)} = 0$ then tan x tan y tan 7 tan t=

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Solution

The correct option is B
-1

$\frac{c o s (x - y)}{c o s (x + y)} + \frac{c o s (7 + t)}{c o s (7 - t)} = 0 \Rightarrow \frac{1 + t a n x t a n y}{1 - t a n x t a n y} + \frac{1 - t a n 7 t a n t}{1 + t a n 7 t a n t} = 0$
$\Rightarrow$ (1+tan 7 tan t +tan x tan y +tan x tan y tan 7 tan t)+(1-tan 7 tan t-tan x tan y+tan x tan y tan 7 tan t)=0
$∴$ 2=-2 tan x tan y tan 7 tan t.
$∴$ tan x tan y tan 7 tan t =-1.

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If cos(x−y)cos(x+y)+cos(7+t)cos(7−t)=0 then tan x tan y tan 7 tan t=

If $\frac{c o s (x - y)}{c o s (x + y)} + \frac{c o s (7 + t)}{c o s (7 - t)} = 0$ then tan x tan y tan 7 tan t=